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Vortices in rotating Bose-Einstein condensates confined in homogeneous traps

We investigate analytically the thermodynamical stability of vortices in the ground state of rotating 2-dimensional Bose-Einstein condensates confined in asymptotically homogeneous trapping potentials in the Thomas-Fermi regime. Our starting point is the Gross-Pitaevskii energy functional in the rotating frame. By estimating lower and upper bounds for this energy, we show that the leading order in energy and density can be described by the corresponding Thomas-Fermi quantities and we derive the next order contributions due to vortices. As an application, we consider a general potential of the form V(x,y) = (x^2+lambda^2 y^2)^{s/2} with slope s \in [2,infinity) and anisotropy lambda \in (0,1] which includes the harmonic (s=2) and 'flat' (s -> infinity) trap, respectively. For this potential, we derive the critical angular velocities for the existence of vortices and show that all vortices are singly-quantized. Moreover, we derive relations which determine the distribution of the vortices in the condensate i.e. the vortex pattern.